In this work, the three-dimensional numerical resolution of a complex mathematical model for the blood coagulation process is presented. The model was illustrated in Fasano et al. (Clin Hemorheol Microcirc 51:1–14, 2012), Pavlova et al. (Theor Biol 380:367–379, 2015). It incorporates the action of the biochemical and cellular components of blood as well as the effects of the flow. The model is characterized by a reduction in the biochemical network and considers the impact of the blood slip at the vessel wall. Numerical results showing the capacity of the model to predict different perturbations in the hemostatic system are discussed.